Statistics Mathl2l A2 More Probability Problems Dr Pendergrass Spring2009 print name ON MY HoNoR I HAVE NEITI ER GIVEN NOR RECEIVEDANY AID oN THIS WORK NOR AM I AWAREOFANY BREACHOF TTm HONOR Coop TTI T I SHALLNOT IMMEDIATELYREPORT pledged Show your work This assignmentis due at the beginning of classon Thursday February 26 Wite up your solutions neatly one problem per page and hand them in with this sheetas a cover page I Supposewe have anuffiir coin whoseprobability of headsis 0 7 We tossthe coin 3 times and recordthe outcomesin order Tossesare still independent so what we get on toss t has no eflect on toss 2 etc Write down the probability model for this experimentas a table Hint use independenceto calculatethe probability of each outcome 2 An urn has 3 red balls and 3 white balls We pick two balls at random from the urn i e we choosean SRS of size 2 LetNbe the number of red balls chosen Find the probability model for n Hint there are 15 possibleoutcomesto this random experiment 3 Below you seethe graph of a probability density function p x for a certain random variableX a What is the value of ft b FindP 0 5 X 1 5 4 Supposethe heights of Hampden Sydneystudentsare normally distributed with mean 69 inches and standarddeviation 2 9 inches Pick a Hampden Sydneystudentat random and let I be his height Find P H 76 5 Calvin s favorite cereal Chocolate CoatedSugarBombs comesin a standardbox that is labeled as containing 32 ouncesof cereal However there is some variability in the actual amount of cerealthat winds up in a box The manufacturersknow that the standarddeviation of the amount of cerealin a box is o 25 ounces How much cerealshould they actually put in the boxes on average in order for the probabilify that a box containslessthan 32 ouncesbe only 0 5Vo r rrLa yk c rt b 14 ftL lil J t I A TA 0 i A il Qr lor 4 t1 f r aj L l i t t Inr N4 L r 1 v t r rL l 1r t 7 h J t b r N Ll t9 z U1 v 2 1 w 3 49 z l I t v I Llfi 1 tltq J 19 L 6 I tl v I I I t v r t4 Lf 5 vv t v 6 t I r ule z t n t rq 4 1 uh fq tL r2b t l6 l ot 1 t L L t V ug o1 og T i1 l t U o1 ta oil n d i 1t tt t Ou Lcttl e t b l I o F bJ l l l n C t l l lrco 1 tt k O A f r l I 2 t t alz n a 4 X 2 nt 7l t v rJ t t1 14 L L 1 7 L 1 b 1 ft t gfo s br64 dD W qz 1 L 7 Ltr t n h c ll j Y1 7 D ooy In n N o r o oo9 o 2 51E5 Jo 1a iM 75 t5h L t 0 f l rL N TL 2 5 n lL L I0q1 14 q4 l u
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